Max has a utility function u(w)=w^0.8 . Max has $1000. He can borrow money at 7% p.a. for one year. Max can invest any sum in an asset which has three possible outcomes:

Annual Return of -15% with probability 0.20

Annual Return of 10% with probability 0.50

Annual Return of 20% with probability 0.30

Assume that Max borrows $L and invests $(1000+L) in this asset. At the end of the year he repays L with interest at 7% p.a

What is the value of L which will maximise his expected utility?